Advertisement

The European Physical Journal A

, Volume 31, Issue 4, pp 534–536 | Cite as

Pseudoscalar meson masses in unitarized chiral perturbation theory

  • J. A. Oller
  • L. RocaEmail author
QNP 2006
  • 29 Downloads

Abstract.

This contribution summarizes the work explained in arXiv:hep-ph/0608290 where we perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. The pseudoscalar self-energies are calculated by the evaluation of the scalar self-energy loops with full S-wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT). These amplitudes, among other features, contain the lightest nonet of scalar resonances σ, f 0(980), a 0(980) and κ. The self-energy loops are regularized by a proper subtraction of the infinities within a dispersion relation formulation of the amplitudes. Values for the bare masses of pions and kaons and the η 8 mass are obtained. We then match to the self-energies from standard Chiral Perturbation Theory (CHPT) to O(p 4) and resum higher orders from our calculated scalar self-energies. The dependence of the self-energies on the quark masses allows a determination of the ratio of the strange-quark mass over the mean of the lightest-quark masses, m s/\( \hat{{m}}\), in terms of the O(p 4) CHPT low-energy constant combinations 2L r 8 - L r 5 and 2L r 6 - L r 4. In this way, we give a range for the values of these low-energy counterterms and for 3L 7 + L r 8, once the η-meson mass is invoked. The low-energy constants are further constraint by performing a fit to the recent MILC lattice data on the pseudoscalar masses, and m s/\( \hat{{m}}\) = 25.6±2.5 results. This value is consistent with 24.4±1.5 from CHPT and phenomenology and more marginally with the value 27.4±0.5 obtained from pure perturbative chiral extrapolations of the MILC lattice data to physical values of the lightest-quark masses.

PACS.

14.65.Bt Light quarks 12.40.Yx Hadron mass models and calculations 14.40.Aq π, K, and η mesons 12.39.Fe Chiral Lagrangians 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Amoros, J. Bijnens, P. Talavera, Nucl. Phys. B 568, 319 (2000).CrossRefADSGoogle Scholar
  2. 2.
    J.A. Oller, L. Roca, arXiv:hep-ph/0608290.Google Scholar
  3. 3.
    C. Aubin, Phys. Rev. D 70, 094505 (2004).CrossRefADSGoogle Scholar
  4. 4.
    C. Aubin, Phys. Rev. D 70, 031504 (2004).CrossRefADSGoogle Scholar
  5. 5.
    H. Leutwyler, Phys. Lett. B 378, 313 (1996).CrossRefADSGoogle Scholar
  6. 6.
    J.A. Oller, E. Oset, Phys. Rev. D 60, 074023 (1999).CrossRefADSGoogle Scholar
  7. 7.
    J.A. Oller, E. Oset, Nucl. Phys. A 620, 438 (1997)CrossRefADSGoogle Scholar
  8. 8.
    J.A. Oller, E. Oset, J.R. Pelaez, Phys. Rev. Lett. 80, 3452 (1998)CrossRefADSGoogle Scholar
  9. 9.
    J.A. Oller, E. Oset, Nucl. Phys. A 629, 739 (1998).CrossRefADSGoogle Scholar
  10. 10.
    U.G. Meissner, J.A. Oller, Nucl. Phys. A 679, 671 (2001)CrossRefADSGoogle Scholar
  11. 11.
    J.A. Oller, E. Oset, J.E. Palomar, Phys. Rev. D 63, 114009 (2001).CrossRefADSGoogle Scholar
  12. 12.
    M. Jamin, J.A. Oller, A. Pich, Nucl. Phys. B 622, 279 (2002).CrossRefADSGoogle Scholar
  13. 13.
    J.A. Oller, Phys. Lett. B 426, 7 (1998)CrossRefADSGoogle Scholar
  14. 14.
    L. Roca, J.E. Palomar, E. Oset, H.C. Chiang, Nucl. Phys. A 744, 127 (2004).CrossRefADSGoogle Scholar
  15. 15.
    E. Oset, J.R. Pelaez, L. Roca, Phys. Rev. D 67, 073013 (2003).CrossRefADSGoogle Scholar
  16. 16.
    J.A. Oller, Phys. Rev. D 71, 054030 (2005).CrossRefADSGoogle Scholar
  17. 17.
    M. Jamin, J.A. Oller, A. Pich, JHEP 0402, 047 (2004)CrossRefADSGoogle Scholar
  18. 18.
    J.A. Oller, U.G. Meissner, Phys. Lett. B 500, 263 (2001).CrossRefADSGoogle Scholar
  19. 19.
    J.A. Oller, Phys. Lett. B 477, 187 (2000).CrossRefADSGoogle Scholar
  20. 20.
    J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 465 (1985).CrossRefADSGoogle Scholar
  21. 21.
    MILC Collaboration (C. Aubin), Phys. Rev. D 70, 114501 (2004).CrossRefADSGoogle Scholar
  22. 22.
    J. Bijnens, G. Colangelo, J. Gasser, Nucl. Phys. B 427, 427 (1994).CrossRefADSGoogle Scholar
  23. 23.
    G. Amoros, J. Bijnens, P. Talavera, Nucl. Phys. B 585, 293 (2000)CrossRefADSGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag 2007

Authors and Affiliations

  1. 1.Departamento de FısicaUniversidad de MurciaMurciaSpain

Personalised recommendations